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Review “Study for Quizzes and Tests”, i
Copyright, iv
Three Distinct Series, xii
Preface to the Instructor, xiii
List of Applications, xix
Photo Credits, xxv
To the Student, xxvii
R. Review, 1
R.1. Real Numbers, 2
R.2. Algebra Essentials, 17
R.3. Geometry Essentials, 30
R.4. Polynomials, 39
R.5. Factoring Polynomials, 49
R.6. Synthetic Division, 57
R.7. Rational Expressions, 61
R.8. nth Roots; Rational Exponents, 72
Chapter Review, 80
Chapter Test, 84
1. Equations and Inequalities, 85
1.1. Linear Equations, 86
1.2. Quadratic Equations, 97
1.3. Complex Numbers; Quadratic Equations in the Complex Number System, 109
1.4. Radical Equations; Equations Quadratic in Form; Factorable Equations, 118
1.5. Solving Inequalities, 124
1.6. Equations and Inequalities Involving Absolute Value, 135
1.7. Problem Solving: Interest, Mixture, Uniform Motion, and Constant Rate Job Applications, 139
Chapter Review, 148
Chapter Test, 152
Chapter Projects, 153
2. Graphs, 155
2.1. The Distance and Midpoint Formulas, 156
2.2. Graphs of Equations in Two Variables; Intercepts; Symmetry, 163
2.3. Lines, 173
2.4. Circles, 189
2.5. Variation, 195
Chapter Review, 201
Chapter Test, 204
Cumulative Review, 204
Chapter Project, 205
3. Functions and Their Graphs, 207
3.1. Functions, 208
3.2. The Graph of a Function, 222
3.3. Properties of Functions, 231
3.4. Library of Functions; Piecewise-defined Functions, 242
3.5. Graphing Techniques: Transformations, 252
3.6. Mathematical Models: Building Functions, 264
Chapter Review, 269
Chapter Test, 274
Cumulative Review, 275
Chapter Projects, 276
4. Linear and Quadratic Functions, 277
4.1. Linear Functions and Their Properties, 278
4.2. Building Linear Functions from Data, 287
4.3. Quadratic Functions and Their Properties, 293
4.4. Quadratic Models; Building Quadratic Functions from Data, 305
4.5. Inequalities Involving Quadratic Functions, 314
Chapter Review, 318
Chapter Test, 320
Cumulative Review, 321
Chapter Projects, 322
5. Polynomial and Rational Functions, 323
5.1. Polynomial Functions and Models, 324
5.2. Properties of Rational Functions, 344
5.3. The Graph of a Rational Function, 355
5.4. Polynomial and Rational Inequalities, 369
5.5. The Real Zeros of a Polynomial Function, 375
5.6. Complex Zeros; Fundamental Theorem of Algebra, 389
Chapter Review, 394
Chapter Test, 398
Cumulative Review, 398
Chapter Projects, 399
6. Exponential and Logarithmic Functions, 401
6.1. Composite Functions, 402
6.2. One-to-One Functions; Inverse Functions, 409
6.3. Exponential Functions, 423
6.4. Logarithmic Functions, 437
6.5. Properties of Logarithms, 450
6.6. Logarithmic and Exponential Equations, 459
6.7. Compound Interest, 465
6.8. Exponential Growth and Decay Models; Newton’s Law; Logistic Growth and Decay Models, 475
6.9. Building Exponential, Logarithmic, and Logistic Models from Data, 487
Chapter Review, 494
Chapter Test, 500
Cumulative Review, 501
Chapter Projects, 502
7. Trigonometric Functions, 503
7.1. Angles and Their Measure, 504
7.2. Right Triangle Trigonometry, 517
7.3. Computing the Values of Trigonometric Functions of Acute Angles, 529
7.4. Trigonometric Functions of General Angles, 540
7.5. Unit Circle Approach; Properties of the Trigonometric Functions, 550
7.6. Graphs of the Sine and Cosine Functions, 560
7.7. Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions, 574
7.8. Phase Shift; Sinusoidal Curve Fitting, 581
Chapter Review, 592
Chapter Test, 598
Cumulative Review, 598
Chapter Projects, 599
8. Analytic Trigonometry, 601
8.1. The Inverse Sine, Cosine, and Tangent Functions, 602
8.2. The Inverse Trigonometric Functions (Continued), 614
8.3. Trigonometric Identities, 620
8.4. Sum and Difference Formulas, 627
8.5. Double-angle and Half-angle Formulas, 637
8.6. Product-to-Sum and Sum-to-Product Formulas, 646
8.7. Trigonometric Equations (I), 649
8.8. Trigonometric Equations (II), 656
Chapter Review, 663
Chapter Test, 666
Cumulative Review, 667
Chapter Projects, 667
9. Applications of Trigonometric Functions, 669
9.1. Applications Involving Right Triangles, 670
9.2. The Law of Sines, 675
9.3. The Law of Cosines, 686
9.4. Area of a Triangle, 691
9.5. Simple Harmonic Motion; Damped Motion; Combining Waves, 697
Chapter Review, 707
Chapter Test, 710
Cumulative Review, 711
Chapter Projects, 711
10. Polar Coordinates; Vectors, 713
10.1. Polar Coordinates, 714
10.2. Polar Equations and Graphs, 722
10.3. The Complex Plane; DeMoivre’s Theorem, 738
10.4. Vectors, 746
10.5. The Dot Product, 757
Chapter Review, 765
Chapter Test, 768
Cumulative Review, 769
Chapter Projects, 769
11. Analytic Geometry, 771
11.1. Conics, 772
11.2. The Parabola, 773
11.3. The Ellipse, 782
11.4. The Hyperbola, 792
11.5. Rotation of Axes; General Form of a Conic, 804
11.6. Polar Equations of Conics, 812
11.7. Plane Curves and Parametric Equations, 818
Chapter Review, 830
Chapter Test, 833
Cumulative Review, 833
Chapter Projects, 834
12. Systems of Equations and Inequalities, 835
12.1. Systems of Linear Equations: Substitution and Elimination, 836
12.2. Systems of Linear Equations: Matrices, 850
12.3. Systems of Linear Equations: Determinants, 865
12.4. Matrix Algebra, 875
12.5. Partial Fraction Decomposition, 891
12.6. Systems of Nonlinear Equations, 898
12.7. Systems of Inequalities, 907
12.8. Linear Programming, 915
Chapter Review, 921
Chapter Test, 925
Cumulative Review, 926
Chapter Projects, 927
13. Sequences; Induction; the Binomial Theorem, 929
13.1. Sequences, 930
13.2. Arithmetic Sequences, 939
13.3. Geometric Sequences; Geometric Series, 945
13.4. Mathematical Induction, 957
13.5. The Binomial Theorem, 961
Chapter Review, 967
Chapter Test, 970
Cumulative Review, 970
Chapter Projects, 971
14. Counting and Probability, 973
14.1. Counting, 974
14.2. Permutations and Combinations, 979
14.3. Probability, 988
Chapter Review, 998
Chapter Test, 1000
Cumulative Review, 1001
Chapter Projects, 1001
Appendix. Graphing Utilities, A1
1 The Viewing Rectangle, A1
2 Using a Graphing Utility to Graph Equations, A3
3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry, A6
4 Using a Graphing Utility to Solve Equations, A8
5 Square Screens, A10
6 Using a Graphing Utility to Graph Inequalities, A11
7 Using a Graphing Utility to Solve Systems of Linear Equations, A12
8 Using a Graphing Utility to Graph a Polar Equation, A13
9 Using a Graphing Utility to Graph Parametric Equations, A14
Answers, AN1
Index, I1
Michael Sullivan: Algebra & Trigonometry, IFC-1
Trigonometric Functions, IBC-1
Prepare for Class “Read the Book”, EP-1
Practice “Work the Problems”, EP-2

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